further mechanics

• newton’s law of restitution/newton’s experimental law in words:

  coefficient of restitution = speed of separation/speed of approach
• newton’s law of restitution/newton’s experimental law as a formula:

  e = (v1 - v2)/(u2 - u1)
• formula for impulse:

  I = mv - mu
• formula for conservation of momentum:

  m1*u1 + m2*u2 = m1*v1 + m2*v2
• change in KE = 0.5m(u^2 - v^2)
• what is the equation for hooke's law in words?

  tension = (modulus of elasticity x extension)/(original lengths)
• when springs are compressed, the tension becomes thrust in the opposite direction of compression.
• when strings are ‘compressed’, they have 0 elastic potential energy.
• when an object is hanging at equilibrium, we call this the equilibrium position, this is where tension = mass x gravity
• when bouncing up and down, the object will oscillate around the equilibrium position, at that position, acceleration is 0 and the object is at its maximum speed.
• what is the formula for elastic potential energy in words?

  ((modulus of elasticity)(extension)^2)/2(original length)
• GPE = mgh
• formula for kinetic energy?

  $\frac{1}{2} \times \text{mass} \times \text{velocity}^2$
• simplified work energy in words

  initial energy + energy in = final energy + energy out
• momentum = mass x velocity
• impulse is the change in momentum.
• impulse is also force x time
• when two objects are in contact with each other, there will be equal and opposite impulses.
• total momentum before collision = total momentum after collision
• power is the rate of work
• power = force x velocity
• what is power measured in?

  Watts
• max. power when acceleration = 0
• when an object has maximum power, the velocity is at its maximum and the resultant forces in either direction are balanced.
• work done = force x distance
• work done is the energy put into the system, and the object gains energy.
• what is work done measured in?

  joules
• newtons second law

  f = ma
• in a two dimensional elastic collision, the parallel component of the velocity is the same before and after the collision
• what are the two dot product formulae for elastic collisions?

  • v•w = u•w
  • v•I = -eu•I

  where w = direction of the wall

  and I = perpendicular to the wall (also known as impulse)